Wind reversals in turbulent Rayleigh-Benard convection

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-Benard convection is theoretically analyzed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range 10(-2)<= Pr <= 10(3) and 10(7)<= Ra <= 10(12), the model has the following features: (i) chaotic reversals may be exhibited at Ra >= 10(7); (ii) the Reynolds number based on the root mean square velocity scales as Re-rms similar to Ra-[0.41...0.47] (depending on Pr), and as Re-rms similar to Pr-[0.66...0.76] (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law omega/(nu L-2)similar to(Pr-(0.64 +/- 0.01)Ra0.44 +/- 0.01). The phase diagram of the model is sketched, and the observed transitions are discussed.